Compressed sensing and quantum system identification

Often, one can much more efficiently and cheaply estimate intricate properties of quantum systems without the need of full quantum state or process tomography. Using the idea of compressed sensing, even full quantum state tomography can be made for low rank states with about the square root of the previously known effort. Here, quantum information ideas are on the one hand guiding principles in work on signal processing. On the other, we provide key tools for certification in the quantum technologies.